Coding super-unit parametric modeling method based on polynomial transfer function

Abstract

The invention discloses a coding super-unit electromagnetic response parameterization modeling method combining a polynomial transfer function and deep neural network incremental learning, and the method achieves the accurate prediction of electromagnetic response through constructing a corresponding relation between a deep neural network learning polynomial transfer function coefficient fused with adaptive homogeneous processing and a coding super-unit structure. A simulation result shows that the electromagnetic response parameter curve predicted by the super-unit in the test set by using the parametric modeling method is highly fitted with a super-unit full-wave simulation result, and the accuracy is superior to that of other traditional methods.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic super unit design, and specifically relates to a coding super unit parameterized modeling method based on polynomial transfer function and deep neural network incremental learning. Background Art

[0002] Metamaterials are man-made materials that are realized by artificially arranging tiny units, and the size of their structural units is much smaller than the wavelength being processed. Compared with natural materials, metamaterials can have a negative refractive index. Their unique electromagnetic properties mainly come from their microstructure rather than the constituent materials themselves. Based on this, researchers have designed novel metamaterial structures such as invisible cloaks and super lenses. However, as a three-dimensional structure, traditional metamaterials usually need to be arranged and processed in three-dimensional space, which will lead to problems such as difficult processing and large volume in actual engineering applications. Therefore, metasurfaces came into being. We regard metasurfaces as two-dimensional structures of metamaterials, which are usually only sub-wavelength thick and composed of sub-wavelength structures with specific electromagnetic responses. Not only do they overcome the above problems, but they also have the advantages of low cost, low loss, and easy processing. The digitally coded metasurface proposed by Academician Cui Tiejun in 2014 allows real-time and large-scale control of the metasurface, making it possible to program the functions of the metasurface. At present, electromagnetic simulation of metasurfaces usually requires the use of numerical simulation software, using traditional numerical analysis methods, and iteratively solving Maxwell's equations, which consumes huge manpower and resources.

[0003] In order to design and optimize electromagnetic metamaterial structures more efficiently, it is necessary to propose efficient electromagnetic optimization technology. Deep neural networks can learn complex function mapping relationships. Researchers apply them to the field of metamaterial design. By taking parameters that can characterize the geometric information of metamaterials as network input, the network can output the corresponding electromagnetic response. This process is called forward prediction. Although the emergence of deep neural networks has effectively solved the complex and time-consuming problem of iterative solution of Maxwell's equations, with the introduction of coded metamaterials, the degree of freedom of their surface structures is higher, and simple deep neural networks can no longer accurately predict the electromagnetic response of coded metasurfaces. More accurate and efficient design methods are urgently needed.

[0004] With the in-depth understanding of transfer functions and S parameters, researchers have found that transfer functions have the ability to use low-dimensional vectors to characterize high-dimensional electromagnetic responses. Therefore, combining transfer functions with deep neural networks has become a new research direction. Traditional neural networks sample electromagnetic response S parameters at equal intervals, which is too large in dimension and too complex in network to fit. However, the parameter dimension of transfer functions is greatly reduced and can accurately characterize electromagnetic responses. Using transfer functions for parameter modeling has a natural advantage in data dimensionality reduction.

[0005] However, unlike the parameters that characterize the geometric structure of the encoded metamaterial, the effective order of the transfer function parameters used to characterize the electromagnetic response is not fixed, which requires the parameters of the transfer function to be homogenized so that the order of each sample is consistent, which is convenient for training the neural network. However, how to change the parameters in the homogenization process and how to ensure the consistency and accuracy of the results is a major problem. The present invention proposes a new modeling method to solve this problem. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to combine the transfer function with a deep neural network, to provide a new parametric modeling method, to design a parametric modeling method for a coding superunit of a polynomial transfer function, to effectively solve the problem of coefficient discontinuity between data with large changes in geometry / coding patterns, and to improve the accuracy of forward prediction of coding superunits.

[0007] Technical solution: In order to solve the above technical problems and achieve the above invention objectives, the present invention proposes an electromagnetic coding metasurface unit structure, which has three layers: a metal top layer, a dielectric layer, and a metal bottom layer, wherein the top layer is a metal resonance layer; the coding pattern area width of the metal top layer is 8 mm, the width of the coding pattern metal copper patch is 0.5 mm, the metal top layer is a centrally symmetrical 16×16 coding matrix, the conductivity σ of the metal copper patch of the metal top layer and the metal backplane of the bottom layer is 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

[0008] Furthermore, the dielectric layer of the electromagnetic coding super unit is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2 mm.

[0009] Furthermore, the real part Re and the imaginary part Im of the electromagnetic response of the electromagnetic coding metasurface unit are related to the amplitude A and the phase The following corresponding relationship exists:

[0010]

[0011]

[0012] In addition, the present invention proposes a coding super unit parameterized modeling method based on any one of the incremental learning and polynomial transfer functions, comprising the following steps:

[0013] S1. Obtain electromagnetic response S parameters and polynomial transfer function coefficients;

[0014] S2. Construct a dataset, which is represented by {Meta k ,a k ,b k ,Hs k}, where Meta k is a 16×16 encoding matrix with central symmetry, used to represent the kth encoding super unit, a k and b k represents the polynomial transfer function coefficient vector of the kth coding superunit, Hs k represents the response of the kth encoding superunit;

[0015] S3, build the coefficient prediction network model of fusion adaptive secondary processing:

[0016] S4. Set the training set {Meta k} train Input the numerator coefficient prediction network, denominator coefficient prediction network and homogeneous vector prediction network for multi-task incremental learning;

[0017] S5. Set the test set {Meta k} test The electromagnetic response within the allowable error range is obtained by inputting it into the three trained networks.

[0018] Furthermore, the method of step S1 is as follows:

[0019] The pole residue transfer function is set to:

[0020]

[0021] Where H(s) represents the electromagnetic response, p i represents the ith pole, r i represents the i-th residue, N represents the number of extreme residue pairs;

[0022] The factored transfer function is of the form:

[0023]

[0024] Among them, p i represents the i-th pole, there are N poles, z i represents the i-th zero point, there are M zero points;

[0025] The numerator and denominator polynomial transfer function is expressed as:

[0026]

[0027] Among them, a i represents the i-th numerator coefficient, the vector a consists of M a coefficients, b i represents the i-th denominator coefficient, and the vector b consists of N b coefficients;

[0028] Import the coding metasurface unit structure into the full-wave electromagnetic simulation software, obtain the electromagnetic response S parameters corresponding to the coding metasurface in batches, and export all the coding superunits and the corresponding electromagnetic response data; the S parameters of the coding superunit samples obtained by the simulation software are H(s), and a set of pole vectors p and residue vectors r are extracted from the S parameters using vector fitting technology, and converted into polynomial transfer function coefficient vectors a and b through MATLAB built-in functions zpk and zp2tf;

[0029] A method of extracting a set of numerator and denominator polynomial transfer function coefficients from the frequency response parameter S, and obtaining vector a and vector b, is to obtain the pole vector p and the residue vector r in the pole-residue transfer function by using the vector fitting method; converting them into the pole vector and the zero vector in the factor transfer function by using the zpk function, and converting them into the coefficient vector a and the coefficient vector b in the numerator and denominator polynomial transfer function by using the zp2tf function;

[0030] The frequency response parameter s is associated with the coefficient vectors a and b through a numerator and denominator polynomial transfer function, where s=j×2πf, j is an imaginary unit, and f is the operating frequency band of the coding super unit.

[0031] Furthermore, the method of step S2 is as follows:

[0032] The dataset is represented as {Meta k ,a k ,b k ,Hs k}, where Meta k is a 16×16 encoding matrix with central symmetry, used to represent the kth encoding super unit, a k and b k Indicates the order is N k The polynomial transfer function coefficient vector of the kth coding superunit is specifically expressed as:

[0033]

[0034] in, represents the numerator coefficient of the i-th order in the k-th coding superunit, represents the denominator coefficient of the i-th order in the k-th coding superunit, k = 1, 2, ..., n f , n f is the number of coded superunit samples, for order N k The kth sample, N min =4 and N max =12 respectively represent the minimum and maximum order of all samples:

[0035]

[0036] And, a k and b k All N max dimensional polynomial transfer function vector, with an effective dimension of N k , Hs k is the spectrum response data of the kth sample with a dimension of 2002, which is obtained by concatenating the real part data of 1001 dimensions and the imaginary part data of 1001 dimensions;

[0037] n f = 40,000 samples, 80% of which are divided into training set samples {Meta k} train , 20% are test set samples {Meta k} test , each sample input is a 16×16 encoding matrix, and the corresponding label is a 12-dimensional numerator polynomial coefficient vector a k , 12-dimensional denominator polynomial coefficient vector b k , 2002-dimensional spectral response vector.

[0038] Furthermore, the method of step S3 is as follows:

[0039] S31, predict the same order numerator and denominator coefficient vector A (k) , B (k) and the homogeneous vector q (k) :

[0040] The inputs of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor are all the encoding matrix Meta of the encoding superunit. k All three network structures use the ResNet18 structure using a residual network, the optimizer is Adam, and the A-Predictor outputs N max The numerator coefficient vector A (k) , B-Predictor outputs N max Denominator coefficient vector B (k) , Q-Predictor output N max ×N k Homogeneous coefficient vector q (k) ;

[0041] S32, convert different order coefficient prediction vectors and

[0042] Homogeneous coefficient vector q (k) Expand the prediction vectors of numerator and denominator coefficients of different orders into prediction vectors of numerator and denominator coefficients of the same order, with an order of N max :

[0043]

[0044] in, represents the i-th numerator coefficient of the k-th coding superunit, represents the i-th denominator coefficient of the k-th coding superunit, represents the i-th homogeneous coefficient of the k-th coding superunit, represents the numerator coefficient of the i-th homogeneous coded superunit of the k-th coding superunit, is the denominator coefficient of the i-th homogeneous K-th coding super unit, M k =N max -N k , M k is homogeneous to N max The number of steps required for the order;

[0045] The homogeneous coefficient vector q (k) Construct an N along the diagonal max ×N k The matrix Q (k) , homogeneous numerator coefficient vector A of the same order (k) Prediction vectors with different order numerator coefficients There is a corresponding relationship:

[0046] A (k) =Q (k) ·a (k)

[0047] Expand to

[0048]

[0049] Use matrix inversion and matrix multiplication methods to convert the predicted values ​​A of the three sub-models (k) , B (k) and q (k) Convert to the corresponding coefficient prediction vector and

[0050]

[0051] S33. Construct a transfer function layer to predict frequency response parameters:

[0052] Use the numerator coefficient prediction network A-Predictor and the denominator coefficient prediction network B-Predictor to get the homogeneous coefficient vector A (k) and B (k) , Meta is obtained indirectly through the polynomial transfer function k The corresponding electromagnetic response H k(s), i.e., the transfer function layer, is constructed into a 2002-dimensional spectral response vector by concatenating the real and imaginary parts of the response.

[0053] Furthermore, the construction of the transfer function layer in step S33 is to calculate the spectrum response function H using the homogeneous numerator coefficient vector generated by the numerator coefficient prediction network A-Predictor and the homogeneous denominator coefficient vector generated by the denominator coefficient prediction network B-Predictor k (s), recorded as:

[0054]

[0055] s=j×2πf

[0056] Wherein, j is an imaginary unit, f is the working frequency band of the coding super unit, and the transfer function layer does not update the parameters.

[0057] Furthermore, the specific method of step S4 is as follows:

[0058] S41, numerator coefficient prediction network A-Predictor, denominator coefficient prediction network B-Predictor and homogeneous vector prediction network Q-Predictor training stage one task T ab :

[0059] Input {Meta k ,a k ,b k} train Training data set, where {a k ,b k} train The network training label, the network output predicted numerator and denominator coefficient vector Let it be task T ab ;

[0060] Input the encoding superunit matrix Meta to A-Predictor, B-Predictor and Q-Predictor k ,k=1,2,...,n f , n f The number of super-unit samples is encoded, and the molecular coefficient network outputs the homogeneous molecular prediction vector A of the same order (k) , after the denominator coefficient network outputs the same order homogeneous denominator prediction vector B (k) , after the homogeneous coefficient network outputs the homogeneous prediction vector q (k) After matrix operation, the output is the prediction vector of the numerator and denominator coefficients Phase 1 Task T ab The loss function L old for:

[0061]

[0062] The calculation formula of MAE is:

[0063]

[0064] Among them, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are expressed as θ A ,θ B ,θ Q , Task T ab The training goal is recorded as:

[0065]

[0066] Back propagation is performed according to the loss function of the task to calculate the gradient of each variable of the three sub-networks. The parameter variables of the three sub-networks are updated and calculated by the optimizer. The training cycle epoch is set to 50, and the network weight is updated to θ A ′,θ B ′,θ Q ′;

[0067] S42, obtain the pseudo-label data generated by the network in stage 1:

[0068] Predict input data Meta through the source model trained in stage 1 k The output value {a′ on the old task k ,b k ′}, which is used as a pseudo label for training the model in stage 2;

[0069] S43, numerator coefficient prediction network A-Predictor, denominator coefficient prediction network B-Predictor, homogeneous vector prediction network Q-Predictor training stage two tasks T Hs :

[0070] Input {Meta k ,a′ k ,b k ′,Hs k} train The training data set, where

[0071] {a′ k ,b k ′,Hs k} train is the network training label, a′ k represents the pseudo label of the numerator coefficient of the kth encoding superunit, b k′ represents the denominator coefficient pseudo label of the kth encoding super unit, and the network outputs the predicted numerator and denominator coefficient vector Recorded as old task T ab and the frequency response prediction vector Let it be the new task T Hs ;

[0072] In the second stage, two tasks are trained simultaneously. The old task T ab The loss function L old for:

[0073]

[0074] New TasksT Hs The loss function L new for:

[0075]

[0076] The calculation formula of MSE is:

[0077]

[0078] Among them, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are expressed as θ A ,θ B ,θ Q , the overall task T ab and T Hs The training goal is recorded as:

[0079]

[0080] Among them, λ is the weight coefficient;

[0081] Incremental learning is performed based on the source model trained in stage 1. Back propagation is performed to calculate the gradients of the variables of the three sub-networks according to the loss function of the task. The parameter variables of the three sub-networks are updated and calculated by the optimizer. The training cycle epoch is set to 150, and the network weight is updated to θ A ″,θ B ″,θ Q ″;

[0082] After two stages of certain training cycles, the three sub-networks will converge, and after convergence, the network outputs the predicted numerator coefficients Prediction denominator coefficient Predicting electromagnetic response

[0083] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0084] (1) The present invention is based on a coefficient prediction model that integrates adaptive homogeneous processing based on polynomial transfer functions. The model aims to learn the mapping relationship between the numerator coefficient and the denominator coefficient of the polynomial transfer function using a neural network. The model includes two independent symmetric sub-networks A-Predictor and B-Predictor with consistent structures and a homogeneous vector prediction model network Q-Predictor, which realizes the parametric modeling and homogeneous processing of the super-unit, and ensures that the deep neural network can accurately characterize the high-dimensional electromagnetic response in a low-dimensional environment.

[0085] (2) The present invention introduces the transfer function coefficient a (k) 、b (k) The prediction error and the prediction error of the electromagnetic response H(s) are optimized simultaneously. A multi-stage fine-tuning training strategy is designed and the loss functions of different stages are designed by introducing non-forgetting learning to achieve incremental learning of model tasks.

[0086] (3) The present invention uses the transfer function coefficient a (k) 、b (k) The prediction of electromagnetic response H(s) is taken as two tasks for model learning, and the model is trained based on task increments, which greatly improves the prediction performance of the model.

[0087] (4) In order to better quantify the model performance, the present invention evaluates the model performance using MSE and regression coefficient respectively. At the same time, in order to verify the performance improvement of the incremental learning strategy without forgetting learning in the present invention, it is also compared with the traditional fine-tuning strategy, which further illustrates that the method mentioned in the present invention is of great significance for network optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 The network model structure diagram and training mechanism of the present invention;

[0089] Figure 2 Schematic diagram of the geometric structure of the coding super unit of the present invention. DETAILED DESCRIPTION

[0090] The technical solution of the present invention is described in detail below through the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0091] Example:

[0092] like Figure 2As shown, the present invention proposes an electromagnetic coding metasurface unit structure, having three layers: a metal top layer, a dielectric layer, and a metal bottom layer, wherein the top layer is a metal resonance layer; the coding pattern area width of the metal top layer is 8 mm, the width of the coding pattern metal copper patch is 0.5 mm, the metal top layer is a centrally symmetrical 16×16 coding matrix, the conductivity σ of the metal copper patch of the metal top layer and the metal backplane of the bottom layer is 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017 mm.

[0093] Furthermore, the dielectric layer of the electromagnetic coding super unit is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2 mm.

[0094] Furthermore, different styles of coding matrices correspond to different electromagnetic responses. The simulation frequency range is set to 8-12 GHz, and the corresponding high-dimensional electromagnetic response is obtained using full-wave simulation software. The real part Re and imaginary part Im of the electromagnetic response of the electromagnetic coding metasurface unit are related to the amplitude A and phase of the electromagnetic response. The following corresponding relationship exists:

[0095]

[0096] In addition, the present invention proposes a coding super unit parameterized modeling method based on any one of the incremental learning and polynomial transfer functions, comprising the following steps:

[0097] S1. Obtain electromagnetic response S parameters and polynomial transfer function coefficients;

[0098] S2. Construct a dataset, which is represented by {Meta k ,a k ,b k ,Hs k}, where Meta k is a 16×16 encoding matrix with central symmetry, used to represent the kth encoding super unit, a k and b k represents the polynomial transfer function coefficient vector of the kth coding superunit, Hs k represents the response of the kth encoding superunit;

[0099] S3, build the coefficient prediction network model of fusion adaptive secondary processing:

[0100] S4. Set the training set {Meta k} train Input the numerator coefficient prediction network, denominator coefficient prediction network and homogeneous vector prediction network for multi-task incremental learning;

[0101] S5. Set the test set {Meta k}test The electromagnetic response within the allowable error range is obtained by inputting it into the three trained networks.

[0102] Furthermore, the method of step S1 is as follows:

[0103] The pole residue transfer function is set to:

[0104]

[0105] Where H(s) represents the electromagnetic response, p i represents the ith pole, r i represents the i-th residue, N represents the number of extreme residue pairs;

[0106] The factored transfer function is of the form:

[0107]

[0108] Among them, p i represents the i-th pole, there are N poles, z i represents the i-th zero point, there are M zero points;

[0109] The numerator and denominator polynomial transfer function is expressed as:

[0110]

[0111] Among them, a i represents the i-th numerator coefficient, the vector a consists of M a coefficients, b i represents the i-th denominator coefficient, and the vector b consists of N b coefficients;

[0112] Import the coding metasurface unit structure into the full-wave electromagnetic simulation software, obtain the electromagnetic response S parameters corresponding to the coding metasurface in batches, and export all the coding superunits and the corresponding electromagnetic response data; the S parameters of the coding superunit samples obtained by the simulation software are H(s), and a set of pole vectors p and residue vectors r are extracted from the S parameters using vector fitting technology, and converted into polynomial transfer function coefficient vectors a and b through MATLAB built-in functions zpk and zp2tf;

[0113] A method of extracting a set of numerator and denominator polynomial transfer function coefficients from the frequency response parameter S, and obtaining vector a and vector b, is to obtain the pole vector p and the residue vector r in the pole-residue transfer function by using the vector fitting method; converting them into the pole vector and the zero vector in the factor transfer function by using the zpk function, and converting them into the coefficient vector a and the coefficient vector b in the numerator and denominator polynomial transfer function by using the zp2tf function;

[0114] The frequency response parameter s is associated with the coefficient vectors a and b through a numerator and denominator polynomial transfer function, where s=j×2πf, j is an imaginary unit, and f is the operating frequency band of the coding super unit.

[0115] Furthermore, the method of step S2 is as follows:

[0116] The dataset is represented as {Meta k ,a k ,b k ,Hs k}, where Meta k is a 16×16 encoding matrix with central symmetry, used to represent the kth encoding super unit, a k and b k Indicates the order is N k The polynomial transfer function coefficient vector of the kth coding superunit is specifically expressed as:

[0117]

[0118] in, represents the numerator coefficient of the i-th order in the k-th coding superunit, represents the denominator coefficient of the i-th order in the k-th coding superunit, k = 1, 2, ..., n f , n f is the number of coded superunit samples, for order N k The kth sample, N min =4 and N max =12 respectively represent the minimum and maximum order of all samples:

[0119]

[0120] And, a k and b k All N max dimensional polynomial transfer function vector, with an effective dimension of N k , Hs k is the spectrum response data of the kth sample with a dimension of 2002, which is obtained by concatenating the real part data of 1001 dimensions and the imaginary part data of 1001 dimensions;

[0121] n f = 40,000 samples, 80% of which are divided into training set samples {Meta k} train , 20% are test set samples {Meta k} test , each sample input is a 16×16 encoding matrix, and the corresponding label is a 12-dimensional numerator polynomial coefficient vector a k, 12-dimensional denominator polynomial coefficient vector b k , 2002-dimensional spectral response vector.

[0122] Furthermore, the method of step S3 is as follows:

[0123] S31, predict the same order numerator and denominator coefficient vector A (k) , B (k) and the homogeneous vector q (k) :

[0124] The inputs of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor are all the encoding matrix Meta of the encoding superunit. k All three network structures use the ResNet18 structure using a residual network, the optimizer is Adam, and the A-Predictor outputs N max The numerator coefficient vector A (k) , B-Predictor outputs N max Denominator coefficient vector B (k) , Q-Predictor output N max ×N k Homogeneous coefficient vector q (k) ;

[0125] S32, convert different order coefficient prediction vectors and

[0126] Homogeneous coefficient vector q (k) Expand the prediction vectors of numerator and denominator coefficients of different orders into prediction vectors of numerator and denominator coefficients of the same order, with an order of N max :

[0127]

[0128] in, represents the i-th numerator coefficient of the k-th coding superunit, represents the i-th denominator coefficient of the k-th coding superunit, represents the i-th homogeneous coefficient of the k-th coding superunit, represents the numerator coefficient of the i-th homogeneous coded superunit of the k-th coding superunit, is the denominator coefficient of the i-th homogeneous K-th coding super unit, M k =N max -N k , M k is homogeneous to N max The number of steps required for the order;

[0129] The homogeneous coefficient vector q (k) Construct an N along the diagonal max ×N k The matrix Q (k) , homogeneous numerator coefficient vector A of the same order (k) Prediction vectors with different order numerator coefficients There is a corresponding relationship:

[0130] A (k) =Q (k) ·a (k)

[0131] Expand to

[0132]

[0133] Use matrix inversion and matrix multiplication methods to convert the predicted values ​​A of the three sub-models (k) , B (k) and q (k) Convert to the corresponding coefficient prediction vector and

[0134]

[0135] S33. Construct a transfer function layer to predict frequency response parameters:

[0136] Use the numerator coefficient prediction network A-Predictor and the denominator coefficient prediction network B-Predictor to get the homogeneous coefficient vector A (k) and B (k) , Meta is obtained indirectly through the polynomial transfer function k The corresponding electromagnetic response H k (s), i.e., the transfer function layer, is constructed into a 2002-dimensional spectral response vector by concatenating the real and imaginary parts of the response.

[0137] Furthermore, the construction of the transfer function layer in step S33 is to calculate the spectrum response function H using the homogeneous numerator coefficient vector generated by the numerator coefficient prediction network A-Predictor and the homogeneous denominator coefficient vector generated by the denominator coefficient prediction network B-Predictor k (s), recorded as:

[0138]

[0139] s=j×2πf

[0140] Wherein, j is an imaginary unit, f is the working frequency band of the coding super unit, and the transfer function layer does not update the parameters.

[0141] Furthermore, the specific method of step S4 is as follows:

[0142] S41, numerator coefficient prediction network A-Predictor, denominator coefficient prediction network B-Predictor and homogeneous vector prediction network Q-Predictor training stage one task T ab :

[0143] Input {Meta k ,a k ,b k} train Training data set, where {a k ,b k} train The network training label, the network output predicted numerator and denominator coefficient vector Let it be task T ab ;

[0144] Input the encoding superunit matrix Meta to A-Predictor, B-Predictor and Q-Predictor k ,k=1,2,...,n f , n f The number of super-unit samples is encoded, and the molecular coefficient network outputs the homogeneous molecular prediction vector A of the same order (k) , after the denominator coefficient network outputs the same order homogeneous denominator prediction vector B (k) , after the homogeneous coefficient network outputs the homogeneous prediction vector q (k) After matrix operation, the output is the prediction vector of the numerator and denominator coefficients Phase 1 Task T ab The loss function L old for:

[0145]

[0146] The calculation formula of MAE is:

[0147]

[0148] Among them, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are expressed as θ A ,θ B ,θ Q , Task T ab The training goal is recorded as:

[0149]

[0150] Back propagation is performed according to the loss function of the task to calculate the gradient of each variable of the three sub-networks. The parameter variables of the three sub-networks are updated and calculated by the optimizer. The training cycle epoch is set to 50, and the network weight is updated to θ A ′,θ B ′,θ Q ′;

[0151] S42, obtain the pseudo-label data generated by the network in stage 1:

[0152] Predict input data Meta through the source model trained in stage 1 k The output value {a′ on the old task k ,b k ′}, which is used as a pseudo label for training the model in stage 2;

[0153] S43, numerator coefficient prediction network A-Predictor, denominator coefficient prediction network B-Predictor, homogeneous vector prediction network Q-Predictor training stage two tasks T Hs :

[0154] Input {Meta k ,a′ k ,b k ′,Hs k} train The training data set, where

[0155] {a′ k ,b k ′,Hs k} train is the network training label, a′ k represents the pseudo label of the numerator coefficient of the kth encoding superunit, b k ′ represents the denominator coefficient pseudo label of the kth encoding super unit, and the network outputs the predicted numerator and denominator coefficient vector Recorded as old task T ab and the frequency response prediction vector Let it be the new task T Hs ;

[0156] In the second stage, two tasks are trained simultaneously. The old task T ab The loss function L old for:

[0157]

[0158] New TasksT Hs The loss function L new for:

[0159]

[0160] The calculation formula of MSE is:

[0161]

[0162] Among them, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are expressed as θ A ,θ B ,θ Q , the overall task T ab and T Hs The training goal is recorded as:

[0163]

[0164] Among them, λ is the weight coefficient;

[0165] Incremental learning is performed based on the source model trained in stage 1. Back propagation is performed to calculate the gradients of the variables of the three sub-networks according to the loss function of the task. The parameter variables of the three sub-networks are updated and calculated by the optimizer. The training cycle epoch is set to 150, and the network weight is updated to θ A ″,θ B ″,θ Q ″;

[0166] After two stages of certain training cycles, the three sub-networks will converge, and after convergence, the network outputs the predicted numerator coefficients Prediction denominator coefficient Predicting electromagnetic response

[0167] When the electromagnetic behavior of the electromagnetic coding super unit in this embodiment is parameterized and modeled according to the above method, 40,000 8×8 0-1 coding matrices are randomly generated in the embodiment, 0 represents the position is air, 1 represents the position is a metal copper patch, and the phase difference between the two is π. The matrix value is subtracted by 0.1 to obtain a matrix of 0.9 and -0.1, and the matrix is ​​extended to 16×16 by the center symmetry to represent the coding super unit Meta k , and obtain the corresponding electromagnetic response Hs through electromagnetic simulation software k , electromagnetic response vector Hs k The dimension is 2002. According to step S1 and step S2, the corresponding polynomial transfer function coefficient vector a is extracted by vector fitting. k and b k .

[0168] The dataset of phase 1 consists of {Meta k ,a k ,b k}, divided into a training dataset of size 32,000 {Meta k ,a k ,b k} train and a test dataset of size 8,000 {Meta k ,a k ,b k} test . Among them, enter Meta k The dimension is 16×16, vector a k and b k The dimensions of are all 12, the minimum effective dimension is 8, and the maximum dimension is 12. k ,b k} is labeled as matrix Meta k The label data.

[0169] According to step S3, the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor and the homogeneous vector prediction network Q-Predictor are constructed. The three network structures all use the ResNet18 structure using the residual network, the optimizer is Adam, and the input is the encoding matrix Meta of the encoding super unit. k , the numerator coefficient network generates a 12-dimensional high-order homogeneous vector The denominator coefficient network generates a 12-dimensional high-order homogeneous vector The homogeneous vector prediction network generates an 8-dimensional vector Convert to a 12×12 Q matrix, and then use matrix inversion and matrix multiplication methods to convert the predicted values ​​of the three sub-models and Convert to the corresponding 12-dimensional coefficient prediction vector and The minimum effective dimension is 4 and the maximum is 12. In stage 1, the training cycle is set to 50 and the learning rate is set to 0.01.

[0170] Phase 2 uses the pre-trained network in Phase 1 to obtain pseudo data labels {a′ k ,b k ′}, construct the data set as {Meta k ,a′ k ,b k ′,Hs k}, divided into a training dataset of size 32,000 {Meta k ,a′ k ,b k ′,Hs k} train and a test dataset of size 8,000 {Meta k ,a′k ,b k ′,Hs k} test .

[0171] The predicted high-order homogeneous numerator and denominator coefficient vectors are input into the transfer function layer to obtain the predicted value of the electromagnetic response. The dimension is 2002. In stage 2, the training cycle is set to 150 and the learning rate is 0.001. After a certain number of training cycles in the two stages, all three sub-networks will converge.

[0172] As shown in Table 1, the incremental learning strategy without forgetting learning has improved performance compared with the traditional fine-tuning strategy based on the test set. The training of the traditional fine-tuning model and the incremental learning model in stage 2 are both based on the same source model pre-trained in stage 1. The mean square error (MSE) and regression coefficient (R) are used to calculate the mean square error (MSE) and regression coefficient (R). 2 The evaluation indicators compare the effects of the two models. It can be seen that the MSE of the polynomial transfer function coefficients a and b and the real part, imaginary part, amplitude and phase of the frequency response obtained by the incremental learning strategy model is smaller than that of the model based on the traditional fine-tuning strategy, and the regression coefficient is larger. The fitting performance of the real part, imaginary part and phase reached 98.928%, 98.973% and 85.346%, respectively, proving that the incremental learning is better than the traditional fine-tuning strategy in the fitting accuracy of the polynomial transfer function coefficients and frequency response.

[0173] Table 1 Performance comparison between incremental learning and traditional fine-tuning strategies

[0174]

[0175] The simulation results show that the polynomial transfer function-based coded super-element parametric modeling method constructed according to this method can highly fit the polynomial transfer function coefficients and the real, imaginary, amplitude and phase parameter curves of the electromagnetic response predicted by the super-element in the test set with the full-wave simulation results of the super-element, verifying the effectiveness and reliability of the proposed method.

[0176] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. An electromagnetic coding metasurface unit structure, comprising a metal top layer, a dielectric layer, and a metal bottom layer, wherein the top layer is a metal resonance layer, characterized in that: The width of the coding pattern area of ​​the metal top layer is 8mm, the width of the coding pattern metal copper patch is 0.5mm, the metal top layer is a centrally symmetrical 16×16 coding matrix, the conductivity σ of the metal copper patch of the metal top layer and the metal backplane of the bottom layer is 5.8+007S / m, and the thickness t2 of the metal top layer and the metal bottom layer is 0.017mm.

2. The electromagnetic encoding metasurface unit structure according to claim 1, characterized in that: The dielectric layer of the electromagnetic coding super unit is a dielectric substrate made of F4B with a relative dielectric constant of 2.65 and a thickness of 2 mm.

3. The electromagnetic encoding super unit according to claim 1, characterized in that: The real part Re and imaginary part Im of the electromagnetic response of the electromagnetic coding metasurface unit and the amplitude A and phase of the electromagnetic response The following corresponding relationship exists:

4. A method for parameterized modeling of a coding super unit based on incremental learning and polynomial transfer function according to any one of claims 1 to 3, characterized in that: The steps include: S1. Obtain electromagnetic response S parameters and polynomial transfer function coefficients; S2. Construct a dataset, which is represented by {Meta k ,a k ,b k ,Hs k }, where Meta k is a 16×16 encoding matrix with central symmetry, used to represent the kth encoding super unit, a k and b k represents the polynomial transfer function coefficient vector of the kth coding superunit, Hs k represents the response of the kth encoding superunit; S3, build the coefficient prediction network model of fusion adaptive secondary processing: S4. Set the training set {Meta k } train Input the numerator coefficient prediction network, denominator coefficient prediction network and homogeneous vector prediction network for multi-task incremental learning; S5. Set the test set {Meta k } test The electromagnetic response within the allowable error range is obtained by inputting it into the three trained networks.

5. The method according to claim 4, characterized in that The method of step S1 is as follows: The pole residue transfer function is set to: Where H(s) represents the electromagnetic response, p i represents the ith pole, r i represents the i-th residue, N represents the number of extreme residue pairs; The factored transfer function is of the form: Among them, p i represents the i-th pole, there are N poles, z i represents the i-th zero point, there are M zero points; The numerator and denominator polynomial transfer function is expressed as: Among them, a i represents the i-th numerator coefficient, the vector a consists of M a coefficients, b i represents the i-th denominator coefficient, and the vector b consists of N b coefficients; Import the coding metasurface unit structure into the full-wave electromagnetic simulation software, obtain the electromagnetic response S parameters corresponding to the coding metasurface in batches, and export all the coding superunits and the corresponding electromagnetic response data; the S parameters of the coding superunit samples obtained by the simulation software are H(s), and a set of pole vectors p and residue vectors r are extracted from the S parameters using vector fitting technology, and converted into polynomial transfer function coefficient vectors a and b through MATLAB built-in functions zpk and zp2tf; A method of extracting a set of numerator and denominator polynomial transfer function coefficients from the frequency response parameter S, and obtaining vector a and vector b, is to obtain the pole vector p and the residue vector r in the pole-residue transfer function by using the vector fitting method; converting them into the pole vector and the zero vector in the factor transfer function by using the zpk function, and converting them into the coefficient vector a and the coefficient vector b in the numerator and denominator polynomial transfer function by using the zp2tf function; The frequency response parameter s is associated with the coefficient vectors a and b through a numerator and denominator polynomial transfer function, where s=j×2πf, j is an imaginary unit, and f is the operating frequency band of the coding super unit.

6. The method according to claim 5, characterized in that The method of step S2 is as follows: The dataset is represented as {Meta k ,a k ,b k ,Hs k }, where Meta k is a 16×16 encoding matrix with central symmetry, used to represent the kth encoding super unit, a k and b k Indicates the order is N k The polynomial transfer function coefficient vector of the kth coding superunit is specifically expressed as: in, represents the numerator coefficient of the i-th order in the k-th coding superunit, represents the denominator coefficient of the i-th order in the k-th coding superunit, k = 1, 2, ..., n f , n f is the number of coded superunit samples, for order N k The kth sample, N min =4 and N max =12 respectively represent the minimum and maximum order of all samples: And, a k and b k All are N max dimensional polynomial transfer function vector, with an effective dimension of N k , Hs k is the spectrum response data of the kth sample with a dimension of 2002, which is obtained by concatenating the real part data of 1001 dimensions and the imaginary part data of 1001 dimensions; n f = 40,000 samples, 80% of which are divided into training set samples {Meta k } train , 20% are test set samples {Meta k } test , each sample input is a 16×16 encoding matrix, and the corresponding label is a 12-dimensional numerator polynomial coefficient vector a k , 12-dimensional denominator polynomial coefficient vector b k , 2002-dimensional spectral response vector.

7. The method according to claim 6, characterized in that The method of step S3 is as follows: S31, predict the same order numerator and denominator coefficient vector A (k) , B (k) and the homogeneous vector q (k) : The inputs of the numerator coefficient prediction network A-Predictor, the denominator coefficient prediction network B-Predictor, and the homogeneous vector prediction network Q-Predictor are all the encoding matrix Meta of the encoding superunit. k All three network structures use the ResNet18 structure using a residual network, the optimizer is Adam, and the A-Predictor outputs N max The numerator coefficient vector A (k) , B-Predictor outputs N max Denominator coefficient vector B (k) , Q-Predictor output N max ×N k Homogeneous coefficient vector q (k) ; S32, convert different order coefficient prediction vectors and Homogeneous coefficient vector q (k) Expand the prediction vectors of numerator and denominator coefficients of different orders into prediction vectors of numerator and denominator coefficients of the same order, with an order of N max : Among them, a i (k) represents the i-th numerator coefficient of the k-th coding superunit, represents the i-th denominator coefficient of the k-th coding superunit, represents the i-th homogeneous coefficient of the k-th coding superunit, represents the numerator coefficient of the i-th homogeneous coded superunit of the k-th coding superunit, is the denominator coefficient of the i-th homogeneous K-th coding super unit, M k =N max -N k , M k is homogeneous to N max The number of steps required for the order; The homogeneous coefficient vector q (k) Construct an N along the diagonal max ×N k The matrix Q (k) , homogeneous numerator coefficient vector A of the same order (k) Prediction vectors with different order numerator coefficients There is a corresponding relationship: A (k) =Q (k) ·a (k) Expand to Use matrix inversion and matrix multiplication methods to convert the predicted values ​​A of the three sub-models (k) , B (k) and q (k) Convert to the corresponding coefficient prediction vector and S33. Construct a transfer function layer to predict frequency response parameters: Use the numerator coefficient prediction network A-Predictor and the denominator coefficient prediction network B-Predictor to get the homogeneous coefficient vector A (k) and B (k) , Meta is obtained indirectly through the polynomial transfer function k The corresponding electromagnetic response H k (s), i.e., the transfer function layer, is constructed into a 2002-dimensional spectral response vector by concatenating the real and imaginary parts of the response.

8. The molding method according to claim 7, characterized in that: The construction of the transfer function layer in step S33 is to use the homogeneous numerator coefficient vector generated by the numerator coefficient prediction network A-Predictor and the homogeneous denominator coefficient vector generated by the denominator coefficient prediction network B-Predictor to calculate the spectrum response function H k (s), recorded as: s=j×2πf Wherein, j is an imaginary unit, f is the working frequency band of the coding super unit, and the transfer function layer does not update the parameters.

9. The method according to claim 8, characterized in that The specific method of step S4 is as follows: S41, numerator coefficient prediction network A-Predictor, denominator coefficient prediction network B-Predictor and homogeneous vector prediction network Q-Predictor training stage one task T ab : Input {Meta k ,a k ,b k } train Training data set, where {a k ,b k } train The network training label, the network output predicted numerator and denominator coefficient vector Let it be task T ab ; Input the encoding superunit matrix Meta to A-Predictor, B-Predictor and Q-Predictor k ,k=1,2,...,n f , n f The number of super-unit samples is encoded, and the molecular coefficient network outputs the homogeneous molecular prediction vector A of the same order (k) , after the denominator coefficient network outputs the same order homogeneous denominator prediction vector B (k) , after the homogeneous coefficient network outputs the homogeneous prediction vector q (k) After matrix operation, the output is the prediction vector of the numerator and denominator coefficients Phase 1 Task T ab The loss function L old for: The calculation formula of MAE is: Among them, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are expressed as θ A ,θ B ,θ Q , Task T ab The training goal is recorded as: Back propagation is performed according to the loss function of the task to calculate the gradient of each variable of the three sub-networks. The parameter variables of the three sub-networks are updated and calculated by the optimizer. The training cycle epoch is set to 50, and the network weight is updated to θ A ′,θ B ′,θ Q ′; S42, obtain the pseudo-label data generated by the network in stage 1: Predict input data Meta through the source model trained in stage 1 k The output value {a′ on the old task k ,b k ′}, which is used as a pseudo label for training the model in stage 2; S43, numerator coefficient prediction network A-Predictor, denominator coefficient prediction network B-Predictor, homogeneous vector prediction network Q-Predictor training stage two tasks T Hs : Input {Meta k ,a′ k ,b k ′,Hs k } train Training data set, where {a′ k ,b k ′,Hs k } train is the network training label, a′ k represents the pseudo label of the numerator coefficient of the kth encoding superunit, b k ′ represents the denominator coefficient pseudo label of the kth encoding super unit, and the network outputs the predicted numerator and denominator coefficient vector Recorded as old task T ab and the frequency response prediction vector Let it be the new task T Hs ; In the second stage, two tasks are trained simultaneously. The old task T ab The loss function L old for: New TasksT Hs The loss function L new for: The calculation formula of MSE is: Among them, y is the true value, is the predicted value, N is the dimension, and the weight parameters of the three sub-network models are expressed as θ A ,θ B ,θ Q , the overall task T ab and T Hs The training goal is recorded as: Among them, λ is the weight coefficient; Incremental learning is performed based on the source model trained in stage 1. Back propagation is performed to calculate the gradients of the variables of the three sub-networks according to the loss function of the task. The parameter variables of the three sub-networks are updated and calculated by the optimizer. The training cycle epoch is set to 150, and the network weight is updated to θ A ″,θ B ″,θ Q ″; After two stages of certain training cycles, the three sub-networks will converge, and after convergence, the network outputs the predicted numerator coefficients Prediction denominator coefficient Predicting electromagnetic response

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